Lifting a prescribed group of automorphisms of graphs

Author:

Potočnik Primož,Spiga Pablo

Abstract

In this paper we are interested in lifting a prescribed group of automorphisms of a finite graph via regular covering projections. Let Γ \Gamma be a finite graph and let A u t ( Γ ) \mathrm {Aut}(\Gamma ) be the automorphism group of Γ \Gamma . It is well known that we can always find a finite graph Γ ~ \tilde {\Gamma } and a regular covering projection : Γ ~ Γ \wp \colon \tilde {\Gamma } \to \Gamma such that A u t ( Γ ) \mathrm {Aut}(\Gamma ) lifts along \wp . However, for constructing peculiar examples and in applications it is often important, given a subgroup G G of A u t ( Γ ) \mathrm {Aut}(\Gamma ) , to find \wp along which G G lifts but no further automorphism of Γ \Gamma does, or even that A u t ( Γ ~ ) \mathrm {Aut}(\tilde {\Gamma }) is the lift of G G . In this paper, we address these problems.

Funder

Javna Agencija za Raziskovalno Dejavnost RS

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference33 articles.

1. Overgroups of primitive groups;Aschbacher, Michael;J. Aust. Math. Soc.,2009

2. Overgroups of primitive groups. II;Aschbacher, Michael;J. Algebra,2009

3. Lie representations and groups of prime power order;Bryant, R. M.;J. London Math. Soc. (2),1978

4. Cambridge Studies in Advanced Mathematics;Dicks, Warren,1989

5. Automorphisms of graphs and coverings;Djoković, D. Ž.;J. Combinatorial Theory Ser. B,1974

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